Variability in exposure over time can induce error in exposure assessment and thereby diminish measures of effect in epidemiologic studies. In a univariate regression model, under expectation, evaluating an effect of exposure yields an 'observed' slope coefficient that is smaller than it should be when exposure is imperfectly measured. The ratio of the 'observed' to the true slope coefficient reflects the attenuation bias and it is well known that it equals the ratio of the variance of the true exposure to the variance of the error-prone exposure measure. Given the different expressions for attenuation bias, different forms of the estimators can be constructed as either a ratio of estimated slope coefficients or as a ratio of estimated variances. In the former case, the estimator is a ratio of normally distributed variates, and in the latter case, a ratio of approximately chi-squared distributed variates. This implies that the two estimators are not equal in distribution and we expect that the degree to which they differ may depend upon sample size, the magnitude of the regression effect, and the degree of variability in the true and measured exposures. Therefore, a primary objective of the proposed investigation will be to examine the distributional behavior of the two estimators of attenuation bias using empirical and analytical methods. Simulation studies will be carried out for distinct combinations of sample size and of the parameters in the regression and measurement error models, and comparisons made. Using analytical methods, the conditional distribution of the ratio of the 'observed' to the true slope coefficient given the error-prone exposure measure and the outcome will be derived and compared to the distribution of attenuation bias expressed as a ratio of variances, which is available in closed form in the literature. A final objective of the proposed investigation will be to quantify the degree of measurement error in measures of exposure, assess the consequences of exposure measurement error in attenuating regression results, and make comparisons on the basis of attenuation bias between multiple exposure measures to the same contaminant. Overall, the findings of the proposed investigation should provide a basis for determining when relevant data can be used to make reliable estimates of measurement error and for comparing the degree of exposure measurement error in multiple measures of exposure collected on groups of workers exposed to a variety of workplace contaminants.